提出新型差分隐私机制，减少随机数消耗并避免浮点漏洞。
Dithered Gaussian Mechanism for Randomness-Efficient Differential Privacy
- 通过直接离散化输出而非噪声分布，提升隐私安全性。
- 所需高质量随机比特数显著降低且与噪声水平无关。
- 适合对隐私和性能敏感的模型训练场景。
我们提出一种新的差分隐私机制——抖动高斯机制，作为离散高斯机制的替代方案，其特点是离散化私有输出而非噪声分布本身。将这种离散化视为高斯机制的后处理，新机制直接继承标准高斯机制的隐私保证，同时避免了因有限精度浮点输出带来的安全漏洞。我们证明该机制具有可证明的随机性效率：通过直接采样离散输出值，实现隐私所需的高质量随机比特数显著减少，并独立于噪声水平。这通过分离两种随机源实现：一个用于隐私关键采样的高质量随机源，以及一个高性能的公开随机源（可能被对手知晓），用于提供随机化离散化的额外随机性。这种分离使使用密码学安全随机数成为可能，且性能损失较小。作为应用，我们研究了使用DP-SGD进行模型训练，表明在仅带来适度实际开销的前提下，可实现加密安全的噪声生成并减少浮点漏洞暴露。
原文摘要 · Abstract (English)
We present the dithered Gaussian mechanism, a novel alternative to the discrete Gaussian mechanism for differential privacy that discretizes the private output rather than the noise distribution itself. By interpreting this discretization as post-processing of the Gaussian mechanism, our construction directly inherits the privacy guarantees of the standard Gaussian mechanism while avoiding vulnerabilities caused by finite-precision floating-point outputs. We show that the mechanism is provably randomness-efficient: by sampling the discretized output values directly, the number of high-quality random bits required for privacy can be reduced significantly and made independent of the noise level. This is achieved by separating the randomness into two sources: a high-quality source used for the privacy-critical sampling step, and a high-performance public source, possibly known to the adversary, that supplies the additional randomness needed for randomized discretization. This separation enables the use of cryptographically secure randomness without substantial performance loss. As an application, we study model training with DP-SGD and show that cryptographically secure noise generation with reduced exposure to floating-point vulnerabilities can be achieved with modest practical overhead.
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